Background The National Nutrition Survey, Japan (NNS-J) provides annual anthropometric information for a whole nation over 50 years. Based on this survey, the mean body mass index (BMI) of Japanese men and elderly women has increased in recent decades, but that of young women has decreased. We examined the effect of birth cohort on this phenomenon.Methods We analysed data from the NNS-J for subjects aged 20–69 years. BMI during 1956–2005 and the prevalence of overweight and obesity (BMI ≥ 25 kg/m2) during 1976–2005 were estimated.Results The BMI increased with age in every birth cohort, with similar increments, and did not peak until 60–69 years of age. However, with cross-sectional age, the BMI usually peaked before 60–69 years of age. The differences among cohorts already existed at 20–29 years of age, and slightly increased in men between 20–29 and 30–39 years of age. The BMI in all male age groups increased from the 1891–1900 through 1971–80 cohorts. However, in women, the figure increased until the 1931–40 cohorts, but later decreased. Changes in prevalence were generally consistent with changes in BMI. The recent increase (decrease in young women) in the mean BMI is attributable to birth cohort, indicating that thinner (fatter) and less recent birth cohorts have been replaced by fatter (thinner) ones.Conclusions A cohort effect was quantitatively demonstrated based on a repeated annual survey. In Japan, the differences in BMI among cohorts were already established by young adulthood.

Each of the nationwide surveys on smoking prevalence that have been conducted annually in Japan since 1949 has folObjective To determine smoking trends in Japan in comparison with lung cancer mortality. Methods Age-specific smoking prevalence among cohorts born between 1897 and 1985 were determined for the period 1949-2010. The percentages of the cohorts born between 1893 and 1979 who initiated smoking early (e.g. before the age of 20 years) were determined. The results were compared against lung cancer mortality rates in people aged 40-84 years belonging to cohorts born between 1868 and 1968. Findings In males, smoking prevalence was generally high, particularly among those born before the late 1950s, and early initiation was fairly uncommon. Early initiation was most common among recent birth cohorts of males, who showed relatively low prevalences of smoking. In females, the prevalence of smoking was generally low and early initiation was very uncommon, particularly among those born in the late 1930s and before the late 1940s, respectively. Recent cohorts of females showed relatively high prevalences of smoking and relatively high percentages of early initiation. In both sexes, lung cancer mortality was generally low but increased over the study period. Conclusion Lung cancer mortality in Japanese males was relatively low given the high prevalence of smoking, perhaps because early initiation was fairly uncommon. Over the last four decades, however, early initiation of smoking has become more common in both sexes. The adverse effect this is likely to have on lung cancer mortality rates has probably not been observed because of the long time lag.

In longitudinal data, a continuous response sometimes shows a profile approaching an asymptote. For such data, we propose a new class of models, autoregressive linear mixed effects models in which the current response is regressed on the previous response, fixed effects, and random effects. Asymptotes can shift depending on treatment groups, individuals, and so on, and can be modelled by fixed and random effects. We also propose error structures that are useful in practice. The estimation methods of linear mixed effects models can be used as long as there is no intermittent missing.

When primary endpoints of randomized trials are continuous variables, the ANCOVA with pre-treatment measurements as a covariate is often used to compare two treatment groups. In the ANCOVA, equal slopes (coefficients of pre-treatment measurements) and equal residual variances are commonly assumed. However, random allocation guarantees only equal variances of pre-treatment measurements. Unequal covariances and variances of post-treatment measurements indicate unequal slopes and, usually, unequal residual variances. For non-normal data with unequal covariances and variances of post-treatment measurements, it is known that the ANCOVA with equal slopes and equal variances using an ordinary least-squares method provides an asymptotically normal estimator for the treatment effect. However, the asymptotic variance of the estimator differs from the variance estimated from a standard formula, and its property is unclear. Furthermore, the asymptotic properties of the ANCOVA with equal slopes and unequal variances using a generalized least-squares method are unclear. In this paper, we consider non-normal data with unequal covariances and variances of post-treatment measurements, and examine the asymptotic properties of the ANCOVA with equal slopes using the variance estimated from a standard formula. Analytically, we show that the actual type I error rate, thus the coverage, of the ANCOVA with equal variances is asymptotically at a nominal level under equal sample sizes. That of the ANCOVA with unequal variances using a generalized least-squares method is asymptotically at a nominal level, even under unequal sample sizes. In conclusion, the ANCOVA with equal slopes can be asymptotically justified under random allocation.

In randomized trials, an analysis of covariance (ANCOVA) is often used to analyze post-treatment measurements with pre-treatment measurements as a covariate to compare two treatment groups. Random allocation guarantees only equal variances of pre-treatment measurements. We hence consider data with unequal covariances and variances of post-treatment measurements without assuming normality. Recently, we showed that the actual type I error rate of the usual ANCOVA assuming equal slopes and equal residual variances is asymptotically at a nominal level under equal sample sizes, and that of the ANCOVA with unequal variances is asymptotically at a nominal level, even under unequal sample sizes. In this paper, we investigated the asymptotic properties of the ANCOVA with unequal slopes for such data. The estimators of the treatment effect at the observed mean are identical between equal and unequal variance assumptions, and these are asymptotically normal estimators for the treatment effect at the true mean. However, the variances of these estimators based on standard formulas are biased, and the actual type I error rates are not at a nominal level, irrespective of variance assumptions. In equal sample sizes, the efficiency of the usual ANCOVA assuming equal slopes and equal variances is asymptotically the same as those of the ANCOVA with unequal slopes and higher than that of the ANCOVA with equal slopes and unequal variances. Therefore, the use of the usual ANCOVA is appropriate in equal sample sizes.